He doesn't mean destroyed as in getting Firefly and X Files taken off the air.
St. Elsewhere had a lot of crossovers and guest stars from other series, so when at the end it turned out to be all dreamed up every other series that there were crossovers with would also be just part of that dream. It is a bit hard to explain in a few sentences so please watch this video if you truly care about this subject only takes five minutes.

That is a map of all the destruction. I'll give you the specifics for the three I mentioned, though.

Firefly: There is actually multiple paths. St Elsewhere --> Cheers --> Frasier --> The John Larroquette Show --> Star Trek: The Next Generation --> Star Trek --> Red Dwarf --> Angel --> Firefly (I can't give the specifics for the rest, but the Blue Sun Corporation (hinted to be behind the Academy, River destroys a shirt with their logo when she attacks Jayne with the knife, Two By Two, Hands of Blue) shows up as a client of Wolfram And Hart when Angel is running it)

X- Files: St. Elsewhere --> Homicide: Life on The Street --> The X-Files and while it doesn't mention it on the map, there was an X-Files/Cops crossover.